The problem of interest arises in settings involving the downlink of cellular systems whereby the information sequence is available at multiple base stations. The invention exploits intelligent transmission of the information bearing signal over the multiple independently fading paths from each transmitting base station to the receiver to provide diversity and thus coverage/reliability benefits to the receiver. One embodiment of the invention draws upon connections between the given setting, where data are available at multiple base stations, and settings involving a single active base station with multiple transmit antennas. In particular, it builds upon the existing body of work on the use space-time block codes (STBCs) for providing diversity in the downlink in the case that a single base station with multiple transmit antennas is employed for transmission.
A large collection of STBCs have been proposed in recent years as a way of providing diversity and/or multiplexing benefits by exploiting multiple transmit antennas in the forward link of cellular systems. Given the presence of N transmit antennas, the typical objective is to design the STBC so as to provide order-N diversity in the system. Typical STBC designs encode blocks of K symbols that are transmitted over each of the N antennas by T samples, where T is greater than or equal N, as well as K. Such STBC designs are described by a T×N STBC matrix, whose (i,j)th entry denotes the sample transmitted by the j-th antenna at time i. Of interest are full-rate schemes, i.e., schemes where the effective data transmission rate R=K/T equals 1 symbol/channel use. Another important attribute of a STBC is its decoding complexity. Although the complexity of arbitrary STBCs is exponential in the size K″ of the jointly encoded symbols, there exist designs with much lower complexity. One such attractive class of designs, referred to as orthogonal space-time codes, can provide full diversity while their optimal decoding decouples to (linear processing followed by) symbol-by-symbol decoding.
In S. Yiu, R. Schober and L. Lampe, “Distributed Block Source Coding,” IEEE GLOBECOM 2005 Proceedings, November 2005, a distributed space-time coding method is presented for providing diversity benefits in the setting of interest. The method exploits a standard order-N diversity STBC together with a base station specific “postcoding” operation.
Orthogonal space-time block code designs are well-known in the art and have the following features: they provide full (order-N) diversity; they allow symbol-by-symbol decoding; and their (column) shortened versions are also orthogonal designs, thus providing such orthogonal designs for system with any number of antennas less than or equal to N.
Despite the obvious advantages of orthogonal STBC designs in a distributed downlink transmission environment, a key shortcoming with this approach stems from its limited applicability, in the form of the limitations it incurs in the transmission parameters. In particular, no (complex) full-rate orthogonal designs exist for more than two antennas. For more information, see H. Jafarkani, Space-Time Coding, Theory and Practice, Cambridge University Press, 2005. Specifically, the maximum transmission rate with an OSTBC for an N>3 transmit-antenna setting is provably upper-bounded by ¾ (H. Wang and X.-G. Xia, “Upper bounds of rates of space-time block codes from complex orthogonal designs,” IEEE Trans. Information Theory, pp. 2788-2796, October 2003). Furthermore, although ¾ rate orthogonal space-time codes have been found for N=3 and N=4 transmit antennas, it is not known whether or not the ¾ rate is achievable for N>4 with the restriction of orthogonal designs. In fact, the highest known rate achievable by systematic (complex) orthogonal STBC designs is ½. Such designs make an inefficient use of bandwidth as they employ only half of the available dimensions in the signal space for transmission.
Quasi-orthogonal space-time block code designs exploit the existence of an orthogonal design for an N transmit-antenna system to provide full-rate designs for a 2 N antenna system. Some designs employ the base (N=2) full rate orthogonal design, referred to as the “Alamouti” scheme, to obtain a full diversity system for N=4, that allows for hierarchical decoding. For more information, see S. M. Alamouti, “A simple transmitter diversity scheme for wireless communications,” IEEE Journal Selected Areas in Communications, pp. 1451-1458, October 1998. For instance, one design encodes two blocks of two symbols at a time over four time slots, where the four transmit antennas are split into two groups/pairs and each of the given two pairs of symbols are used independently to construct two Alamouti (N=2) space-time codes. In the first two time slots, each of the two antenna groups signals one of the two “Alamouti” codes and swap for the next two slots. Provided the second set of symbols is from a properly rotated constellation, these designs achieve full diversity and hierarchical decoding.
The use of distributed space-time block codes based on postcoders was introduced in S. Yiu, R. Schober and L. Lampe, “Distributed Block Source Coding,” IEEE GLOBECOM 2005 Proceedings, November 2005. In their technique, each active base station exploits the same space-time block for signaling. In particular, given a T×N space-time block code designed to send blocks of K symbols over n antennae at rate K/T, and given a symbol sequence that is to be transmitted, each base station generates first the common code T×N STBC matrix as if there were a single “active” base station with N transmit antennas. The signal transmitted by the single antenna of an “active” base station is then a linear combination of the columns of the T×N STBC matrix. This linear combination is specific to the particular antenna at the particular base station and can be conveniently expressed as a “projection” of the common STBC onto a base-station specific “steering” vector. Given a set of Mmax single-antenna base-stations, each of which can be potentially “active”, the set of Mmax steering vectors can be jointly optimized a priori, e.g., by use of an LMS algorithm. The resulting set of optimized steering vectors allows the following: given any M out of Mmax base stations are “active” (regardless of which “M” are “active”), with M greater or equal to N, the distributed scheme provides order-N diversity, i.e., the full diversity of the original STBC code. Furthermore, via the joint optimization of the steering vectors the worst-case loss in coding-gain-distance performance with respect to the standard STBC can be minimized.
Although the above approach has a number of advantages, it also has two main drawbacks. First, the larger the set of potentially active steering vectors, the higher the performance loss with respect to the standard code performance. Hence, there is a need for approaches that are scalable, i.e., approaches that scale well with changing M. The joint optimization of the set of potentially active steering vectors proposed in S. Yiu, R. Schober and L. Lampe, “Distributed Block Source Coding,” IEEE GLOBECOM 2005 Proceedings, November 2005, is not scalable. Second and more important, the diversity benefits of the approach are limited by the strength of the standard STBC code employed in the design. Thus, if the well known “Alamouti” code, is employed (designed for a two antenna system), the system provides diversity of order at most 2 even if M, the number of “active” cooperating transmit antennas may be much larger than 2.